Modeling Backlash-Like Hysteresis and Feedforward Control of Tendon−Sheath Mechanism Pair with Arbitrary Shape: Excluding Distal Sensory Input

The tendon−sheath mechanism (TSM) has garnered attention for its versatile applications in soft robotics, robotic hands, and surgical robots due to its adeptness in transmitting force through tortuous and narrow channels. However, the precise control of the TSM is challenging due to its shape-dependent deformation and force generation, highlighting the need to address shape variations in dynamic environments where direct measurement is impractical. This article introduces a novel methodology leveraging the concept of the equivalent circle in TSM to model its shape under varying conditions. The equivalent circle substitutes an arbitrarily shaped TSM with a circle, whose radius is derived from TSM's deformation and forces measured at the proximal end during calibration. This approach provides a concise and effective framework for understanding and analyzing the distinct characteristics of TSM. Additionally, a control strategy is proposed, utilizing the estimated equivalent circle to adapt to dynamic environments. Experimental results demonstrate promising performance without distal end sensory feedback, with mean percentage errors (MPE) of 0.78% and 2.33% for predicting cumulated curve angle and equivalent circle radius, respectively. Moreover, by utilizing the equivalent circle to calculate and feedforward deadband, effective control is achieved. The root mean square error (RMSE) reduced from 1.31 mm to an average of 0.19 mm in two feedforward experiments, representing an average reduction of 85.5%. These findings shed light on effective control strategies for TSM, offering valuable insights for robotics and surgical applications where TSM shape configurations are uncertain and subject to dynamic change.